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Licentiate thesis: Magnetic Helicity Fluxes and their Effects in Dynamo Theory
The roles of magnetic helicity and magnetic helicity fluxes in astrophysical
objects are investigated using various models and field configurations.
Their roles in dynamo theory are confirmed through magnetohydrodynamic
simulations both within the framework of mean-field theory and in
direct numerical simulations.
The constraint of magnetic helicity conservation in a periodic system
at high magnetic Reynolds numbers is analyzed for setups of three
magnetic flux rings which can be interlocked. The linking is able to hinder
the magnetic field to decay only if the linking implies magnetic helicity.
If the magnetic field is not helical
the decay shows the same behavior irrespective of the actual
linking of the rings
which supports the assumption that only the magnetic helicity is the decisive
topological quantity in magnetic relaxation.
The regime of high magnetic Reynolds numbers is analyzed by using a
one-dimensional mean-field model for a helically forced dynamo.
A wind with linear profile is imposed such that magnetic helicity can be
advected to one of the domain boundaries. It is shown that with vacuum
boundary conditions helicity can be shed from of the domain, which
alleviates the quenching at high magnetic Reynolds numbers.
Additionally the same boundary is closed for a different setup where
a diffusive flux is allowed at the midplane of the system.
This is shown to also
reduce the quenching mechanism and to allow for dynamo action at
large magnetic Reynolds numbers.
The influence of the gauge on magnetic helicity transport and fluxes is
explored in the Weyl gauge, the resistive gauge and the pseudo-Lorenz gauge
as well as a newly introduced advecto-resistive gauge. In the first three
gauges spatially averaged fluxes are analyzed and compared with the
one-dimensional mean-field model. The alleviation of the quenching is
independent of the gauge as it was expected since it is a physical effect.
In the advecto-resistive gauge magnetic helicity density evolves like a
passive scalar in the kinematic regime owing it to the advective
nature of the gauge. In the dynamical regime magnetic helicity
is advected into length scales of the turbulent eddies.